Fuzzy Bigraphs: An Exercise in Fuzzy Communicating Agents

Bigraphs and their algebra is a model of concurrency. Fuzzy bigraphs are a generalization of birgraphs intended to be a model of concurrency that incorporates vagueness. More specifically, this model assumes that agents are similar, communication is not perfect, and, in general, everything is or happens to some degree.Comment: 11 pages, 3 figure

Globalisation and the rise of india and china: challenges and opportunities for the East Midlands

Review of literature around the recent (late 20th Century) phase of globalisation, with particular focus on the developing economies of India and China. Includes an economic and policy review of the East Midlands - identifying business and strategic challenges/opportunities for the region

GAIT BIOMECHANICS AND TIBIAL STRESS FRACTURE IN RUNNERS

INTRODUCTION: Stress fractures are a common injury in athletes in general, and runners in particular. Stress fractures are a chronic, or overuse, injury resulting from fatigue damage to the bone. They occur when the damage accumulated due to the repeated application of physiological loads exceeds the capacity of the bony tissue to repair itself. The incidence of stress fractures in athletic populations is up to 50% (Brukner et al., 1996). Tibial stress fractures in particular are very common in recreational and competitive runners and military recruits. The tibia is the most common site of stress fracture in distance runners, accounting over 40% of all stress fractures (Brukner et al., 1996). The typical recovery time from a stress fracture is between 6 and 12 weeks. This includes periods of rest and reduced activity, to allow the natural reparative process of bone to take place at a rate exceeding that of damage accumulation. Reduced training capacity for a period of two to three months is a significant amount of time for both runners and military recruits. Therefore, identification of injury mechanisms and the prevention of stress fractures in runners is an important area of study. RISK FACTORS: Many risk factors for stress fracture have been proposed. Some of these factors are intrinsic to the individual athlete; some are extrinsic and related to environmental factors. Many risk factors can be modified, whereas others can only be accommodated. Proposed extrinsic factors include those related to training, including the volume per session and per week, intensity level, running surface, and recent changes in the program (Bennell & Brukner, 2005). These factors can be modified, although other considerations such as competition scheduling or basic training requirements may influence this. Proposed intrinsic factors include anatomical structure of the lower extremity, muscle strength, flexibility, menstrual status, bone density, diet and nutrition, and running biomechanics (Bennell & Brukner, 2005). In order to investigate contributions to stress fracture risk from biomechanical factors, other risk factors should be standardized as much as possible between comparison groups. GAIT BIOMECHANICS: A series of investigations into the biomechanics of running in relation to tibial stress fracture have been conducted. The aim of these studies was to determine objectively whether running biomechanics are different in those who have sustained a tibial stress fracture compared to those with no previous lower extremity bony injuries. This may enable identification of those at increased biomechanical risk of tibial stress fracture and of potential strategies to reduce their risk by modification of these factors. In cross-sectional studies the influence of potential confounding factors can be reduced by matching characteristics of the participants across comparison groups. Factors including age, height, weight, sex, footstrike pattern, and monthly running mileage can be matched to reduce the variability between groups due to these potentially confounding factors. Given that tibial stress fracture is an overuse injury due to fatigue of bone tissue, early work in this area focused on loading characteristics of gait, primarily ground reaction forces. Studies focusing on peak ground reaction forces were inconclusive, with some indicating greater peak values after tibial stress fracture compared to controls (Grimston et al., 1991) and others finding no difference (Crossley et al., 1999; Bennell et al., 2004). However, greater loading rates were found in runners with a previous tibial stress fracture compared to matched control runners (average vertical loading rate 79.0BW/s vs. 66.3BW/s, P = 0.041; instantaneous loading rate 92.6BW/s vs. 79.6BW/s, P = 0.036; Milner et al., 2006a). Additionally, a more direct measurement of tibial loading, tibial shock (peak acceleration) measured using an accelerometer, also supported the hypothesis of increased loading of the tibia in those susceptible to tibial stress fracture compared to controls (7.7g vs. 5.8g, P = 0.014). However, further analysis indicated that tibial shock explained only 17% of the variance between tibial stress fracture and control groups. This finding supported the hypothesis that the risk of tibial stress fracture is multifactoral, and that other biomechanical factors are likely involved. FREE MOMENT: During running, the tibia is exposed simultaneously to a combination of shearing, bending and torsional loads, in addition to compression (Ekenman et al., 1998). While vertical ground reaction forces and tibial shock may provide an indication of the compressive load applied to the tibia, they do not indicate torque about the vertical axis. The free moment of ground reaction force indicates this torque at the point of contact of the runner with the ground (Milner et al., 2006b). Thus, it may provide an indirect measure of the torque acting on the tibia. Comparison of the magnitude of peak free moment during the stance phase of running between those with previous tibial stress fracture and matched controls indicated greater values in the stress fracture group (9.3 x 10-3 vs. 5.9 x 10-3Nm/BW*ht, P < 0.001). Further analysis suggested that this variable explained 27% of the variance between the two groups. It’s important to note that the majority of runners exhibit an adduction bias in the direction of free moment during the stance phase of running (i.e. resisting toe out torque of the foot on the ground). This torque has been associated with pronation (eversion) in the literature (Holden and Cavanagh, 1991). These loading-related variables that exhibit differences during running between runners with a previous tibial stress fracture and matched controls occur in the earlier part of stance phase. During early stance, body weight is shifted rapidly onto the stance limb. Therefore, studying lower extremity biomechanics during this period of rapidly increasing loading may be critical in understanding differences between runners susceptible to tibial stress fracture and healthy controls. INITIAL LOADING: Higher vertical ground reaction force loading rates and higher tibial shock have been found in runners with previous tibial stress fracture compared to matched controls. The effect of external loading on the body can be modulated by body’s the response to it. A good example is jumping off a wall onto the ground: landing in a stiff posture with knees maintained in extension results in higher loads transmitted through the body than landing with a large range of flexion motion at the lower extremity joints. In this respect, the knee is often considered to be of primary importance as a damper during landing. During running, each stance phase can be considered a single-legged landing, since the runner moves from a flight phase to single limb support. Thus, the initial loading part of the stance phase, from foot contact to the impact peak of vertical ground reaction force, may be important in terms of factors relating to tibial stress fracture. Vertical loading rate, which is calculated over the initial loading period, is greater in runners with a previous tibial stress fracture compared to controls (Milner et al., 2006a). Therefore, the body’s response, in particular at the knee, to the high rate of loading during early stance may be an important consideration in injury risk. Knee joint stiffness was indeed found to be greater in runners with previous tibial stress fracture compared to controls (0.044Nm/(mass*ht) vs. 0.030 Nm/(mass*ht), P = 0.015; Milner et al., 2007). It was also positively correlated with tibial shock. However, there was only a moderate relationship in the stress fracture group between knee stiffness and tibial shock (r = 0.406). In the control group, the relationship was weak (r = 0.161). Thus, the body’s response to loading during the early part of stance phase may also be important in understanding the complex relationship between loading and the occurrence of tibial stress fracture. PROXIMAL AND DISTAL FACTORS: While several studies have focused on ground reaction forces and tibial shock measures in relation to tibial stress fracture, it should be remembered that the lower extremity is a linked chain with several joints and segments. The position of each lower extremity joint is important in determining the position of each segment. While static alignment factors in general have not shown strong association with tibial stress fracture, there is some evidence that extremes of foot type (very high or very low arches) may increase the risk of tibial stress injuries (Barnes et al., 2008). It has been suggested that dynamic alignment during the stance phase of running may be important in relation to stress fracture (Bennell & Brukner, 2005). Abnormal joint kinematics within the lower extremity chain may contribute to abnormal distribution of musculoskeletal loads, including within the tibia. Both proximal and distal joint kinematics may contribute to the combination of factors predisposing some runners to tibial stress fracture, even in the presence of normal loads. Altered frontal and transverse plane joint positions may change the axial, bending and torsional loads in the tibia. Several important differences were found in a comparison of frontal and transverse plane kinematics at the hip, knee, and ankle in female runners (Milner et al., in review). In particular, peak rearfoot eversion (11.7° vs. 9.0°, P = 0.015) and peak hip adduction (11.6° vs. 8.1°, P = 0.004) were both several degrees greater in runners with previous tibial stress fracture compared to controls with no previous bony injuries.This ties in with other work that found peak hip adduction, peak rearfoot eversion and the absolute free moment were the most important predictors of previous tibial stress fracture in distance runners (Pohl et al., 2008). Currently, it cannot be determined whether the differences in the frontal plane at the hip are a proximal compensation for the distal differences in the frontal plane at the rearfoot or vice versa. DISCUSSION: While many factors, both internal and external to the runner, likely play a role in the development of tibial stress fractures, several biomechanical variables have been associated with this injury. It should be noted that the studies reported were retrospective and cross-sectional in design. Therefore, it cannot be determined whether the biomechanics of runners with a previous stress fracture measured after recovery from the injury are the same as prior to the stress fracture. While this is a limitation in relation to predisposing factors for tibial stress fracture, a large proportion of runners suffer multiple stress fractures after the initial occurrence. Thus, the information obtained in these studies is directly applicable to the case of recurring stress fractures. Future prospective studies may be able to confirm whether the high risk biomechanical features of running were also present in runners with tibial stress fracture prior to their injury. Primarily, several loading-related variables and joint angles have been identified and found to be greater in runners with a previous tibial stress fracture compared to runners with no previous bony injury. In terms of loading, the literature is somewhat inconclusive with regard to ground reaction force variables. While it seems intuitive that bony injury and fatigue fracture (i.e. stress fracture) are associated with damaging loads that exceed the body’s ability to repair itself, tibial loading is only indirectly linked to ground reaction force variables. However, it appears that vertical loading rates (Milner et al., 2006a) and the absolute free moment (Milner et al., 2006b) may be increased in runners with previous tibial stress fracture. These variables may be providing an indication of the magnitude of compression and torsional loads that the tibia is subjected to during the stance phase of running. Given the lower magnitudes of these variables in healthy runners compared to those with a previous stress fracture, these aspects of running biomechanics may be modifiable. Decreasing their magnitude may decrease the risk of injury in susceptible runners. Similarly, the kinematic differences observed and abnormal peak angles reported at the hip and rearfoot in runners with previous tibial stress fracture (Milner et al., in review) may also be modifiable. Although a detailed consideration of interventions to modify running biomechanics is beyond the scope of this paper, several options may be considered. These may be mechanical or functional interventions. Potential mechanical interventions include orthotics or specialized footwear, or changing the running surface. Possible functional interventions include various types of instruction to retrain gait. CONCLUSION: While acknowledging the limitations of retrospective cross-sectional studies, several biomechanical variables have been identified as having greater magnitude during running in those with previous tibial stress fracture compared to controls. Loading-related variables include vertical ground reaction force loading rates, the magnitude of peak free moment, and peak tibial shock. Kinematic variables include peak knee flexion stiffness during initial loading, peak rearfoot eversion and peak hip adduction

The diet and behaviour of hill sheep

The hill lands of Gt. Britain occupying one third of the agricultural acreage produce only about 4% of the total agricultural output. This same area however produces some 30% of the sheep and sheep products of the country. (Davidson & Wibberley, 1956)The key therefore to the economic stability of agriculture in the hills is the hill sheep, for although an increasing number of cattle are being kept, it is difficult in many areas to overcome the problem of Winter keep.The hill environment is considerably more adverse than that of the lowland and the hill ewe is required to survive the winter on an insufficient diet while satisfying the demands of the foetus at a most critical period of development. (Wallace, 1948) For these reasons the hill ewe has been the subject of various investigations based mainly on supplementation of the meagre winter diet.The basic problem however is the interrelation between the sheep and its pasture. Ewes kept on virtually unrestricted hill grazings are able to exercise considerable choice both of the plant communities and species grazed. Under such conditions the factors that determine the distribution of the ewes over the hill are of considerable importance in determining the environment of the individual ewe. Social and flock behaviour is more evident under the low stocking rates encountered and the conditions may therefore be described as semi-natural. It is with this aspect of hill sheep production that the present thesis is mainly concerned.The diversity of the hill sward, which provides the nutrient requirements of the sheep, imposes on them a diversity of nutritional levels and is therefore likely to be one of the most important environmental factors influencing productivity.The basic problem of hill farming is the efficient utilisation of a semi-natural environment. The animal most frequently used for this purpose is the sheep and it is with sheep and their utilisation of hill pastures that this thesis has been concerned. The heft is a complex ecosystem of several sward types grazed at different intensities and pro¬ ducing varying amounts of animal nutrients. The factors governing the grazing intensity and productivity of various communities are not simply those inherent in the coramunity although these are of some importance. Social factors resulting in a non-random distribution of the sheep over the available pasture have been demonstrated and the importance of the home range of the ewes in determining the home range of the lamb shown. This obviously has a considerable effect on the uti¬ lisation of the different communities particularly since up to the present time no account lias been taken of the home range of a ewe and lamb when selecting replacement breeding stock. This has resulted in the selection of lambs from better environments rather than lambs of possibly superior breeding merit. The extent of the environmental difference cannot be accurately determined but sufficient has been produced to show that it is likely to be a very potent source and possibly the most import¬ ant source of variation in the flock.The chief conclusion of this thesis must be that without prior consideration of the complex factors governing the grazing of hill pastures, improvement is blind and may only be of short term value. The Increased productivity of a hill flock and of a hill sward is essentially an ecological problem and should be treated so. The preliminary results in this thesis are an attempt at a solution of some of the ecological problems involved

Prehension and perception of size in left visual neglect

Right hemisphere damaged patients with and without left visual neglect, and age-matched controls had objects of various sizes presented within left or right body hemispace. Subjects were asked to estimate the objects’ sizes or to reach out and grasp them, in order to assess visual size processing in perceptual-experiential and action-based contexts respectively. No impairments of size processing were detected in the prehension performance of the neglect patients but a generalised slowing of movement was observed, associated with an extended deceleration phase. Additionally both patient groups reached maximum grip aperture relatively later in the movement than did controls. For the estimation task it was predicted that the left visual neglect group would systematically underestimate the sizes of objects presented within left hemispace but no such abnormalities were observed. Possible reasons for this unexpected null finding are discussed